Large-Strain Generalization of Microplane Model for Concrete and Application

The formulation of the microplane model for concrete and development of model M4 in the three preceding companion papers in this study is here extended to large strains. After giving examples of certain difficulties with the second Piola-Kirchhoff stress tensor in the modeling of strength and frictional limits on weak planes within the material, the back-rotated Cauchy (true) tensor is introduced as the stress measure. The strain tensor conjugate to the back-rotated Cauchy (or Kirchhoff) stress tensor is unsuitable because it is nonholonomic (i.e., path-dependent) and because its microplane components do not characterize meaningful deformation measures. Therefore Greenʹs Lagrangian tensor is adopted, even though it is not conjugate. Only for this strain measure do the microplane components of the strain tensor suffice to characterize the normal stretch and shear angle on that microplane. Using such nonconjugate strain and stress tensors is admissible because, for concrete, the elastic parts of strains as well as the total volumetric strains are always small, and because the algorithm used guarantees the energy dissipation by large inelastic strains to be nonnegative. Examples of dynamic structural analysis are given.